Sea trial of prototype vertical weight stabilizer (VWS) anti-rolling system for small ships

J Mar Sci Technol (2014) . 19:292-301 D O I IOT007/S00773-013-0248-8

O R I G I N A L A R T I C L E

Sea trial of prototype Vertical Weight Stabilizer (VWS)

anti-rolling system for small ships

Y o s h i a k i H i r a k a w a • Tsugukiyo H i r a y a m a • K o u j i Kakizoe • T a k e h i k o T a k a y a m a •

Shigeru F u n a m i z u • Naoki O k a d a • A k i k o Y a m a n e

Received: 26 February 2013/Accepted: 19 December 2013/Pubhshed online: 5 January 2014 © J A S N A O E 2014

Abstract A n t i - r o l l i n g is an iinportant technique f o r safety

and efficient ship operation. I n the era o f sailing ships, r o l l i n g motions were not so severe compared to those o f modern ships runiung by prime mover w i t h o u t sails, because the sail itself had a damping effect o n r o l l i n g motion. A f t e r propeller driven ships exceeded sailing ships i n number and peiformance, namely, f r o m the end o f the nineteenth century, many types o f anti-rolling-related techniques were invented and developed, o f both passive and active types. Recently (2009, 2010), as sea trials, we caiTied out proto-type experiinents on an anti-rolling system and confirmed its effectiveness. The new concept utilizes the so-cahed C o r i o l i ' s effect, w h i c h appears i n the rota-tional coordinate system. Usually, this effect is considered as virtual, but the real effect appears when a mass moves i n the radial direction i n a rotating coordinate system. I n the case o f ship r o l l i n g , the vertical m o t i o n o f a mass generates C o r i o l i ' s force to finally generate anti-rolling moment. This is the reason the system was named Vertical W e i g h t Sta-bilizer ( V W S ) . This new system was invented i n 1998 by Hirayama, and confirmed by the model experiinents i n a t o w i n g tank. N u m e r i c a l simulations were carried out by the Sea and A i r Control System laboratory o f Yokohama National University, but the actual system could not be realized, because we could not find an appropriate actuator. The key technology f o r the success o f the current sea

Y . Hirakawa ( E l ) • T. Hirayama • K . Kakizoe • T. Takayama Department o f Ocean and Space Systems Engineering, Yokohama National University, Tokiwadai 79-5, Hodogayaku, Yokohama, Kanagawa 240-8501, Japan

e-mail: hirakawa@ynu.ac.jp

S. Funamizu • N . Okada • A . Yamane

College o f Engineering, Yokohama National University, Yokohama, Japan

experiment is the p o w e r f u l , high-speed, compact actuator f o r the vertical movement o f the weight. I n this paper, we introduce this new concept by adopting a simple experi-ment, the control system w i t h new actuator used i n an actual sea experiment, and report on the successful results.

K e y w o r d s A n t i - r o l l i n g • W e i g h t stabilizer • V e r t i c a l

type • Sea t r i a l

1 Introduction

Ship m o t i o n s — f o r example, heaving, p i t c h i n g and r o l l -ing—are not welcome f o r ship operation as they are one reason f o r sea sickness. A m o n g the six modes o f ship m o t i o n , r o l l i n g is very sensitive to damping force, because wave-making damping is very small and eddy-making damping is also smaU w i t h o u t a bilge keel. T h i s means that a more e f f e c t i v e anti-rolling device can be f o u n d than f o r other modes o f m o t i o n .

As an anti-rolling device, the bilge keel is the most simple, e f f e c t i v e and common tool. I t was invented b y W . Froude around the year 1870, and is representative o f the so called passive type. As f o r active types, the fin stabilizer is n o w common, but this is not effective under resting con-ditions. A so-called weight stabilizer (weight is m o v e d i n the horizontal direction) and gyro-stabilizer is e f f e c t i v e even under resting conditions, but is not o f t e n used [ 1 ] .

Aside f r o m these weight stabilizers, Hirayama [ 2 ] invented a new one. I n this new system, the weight is m o v e d i n a vertical direction instead ofa horizontal direc-tion. W e call this a Vertical Weight Stabilizer ( V W S ) . W h y such m o t i o n can generate anti-rolling moment is described i n Sect. 3 o f this paper. This invention was c o n f i r m e d b y a model experiment i n a towing tank and by numerical

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simulation (Hirayama et al. [ 3 ] ) , but an actual experiment could not be realized u n t i l recently. I n order to realize an actual experiment, a p o w e r f u l and high speed actuator was needed, and a recently developed actuator named Zip-chain f u l f i l l e d our requirement [ 4 - 6 ] .

A p p l y i n g the new actuator, we carried out a tank experiment using a r o w i n g boat, then we carried out actual sea experiments, and c o n f i r m e d the ability o f our V W S . I n this paper, we introduce a laboratory experiment describing the existence of r o l l damping by the linear m o t i o n o f a weight inside a swinging pipe. Furthermore, we show the detailed energy dissipation by V W S ; this was not reported i n former papers.

2 Roll damping by weight motion

m o t i o n o f the weight can be seen i n F i g . 2b. The m o t i o n o f the weight fades away after around 15 s have passed. So, after this swinging, the angles o f cases 1 and 2 become similar.

T h e damping that appeared i n the cases o f 3 , 4 , and 5, is considered as t h e result o f air damping and f r i c t i o n around the p i v o t i n g point, w h i c h are very small compared to the cases 1 and 2. Therefore, it is considered that the additional damping should be generated by the m o t i o n o f the weight inside the pipe. I t can be seen that the damping e f f e c t o f the oscillating weight inside the swinging pipe is d i f f e r e n t i f the i n i t i a l position o f the weight is d i f f e r e n t (cases 1 and 2 ) . The physical descriptions of the phenomena that appear i n the rotating coordinate system are made i n the f o l l o w i n g section.

R o l l damping w i l l be generated b y the vertical movement o f a weight along the rhast o f a ship. I n order to show the existence of damping moment by vertical weight move-ment, we carried out a p r i n c i p a l experiment f o r this.

As shown i n F i g . 1, a weight is suspended by a spring inside an acrylic pipe. This pipe substitutes f o r the mast o f a ship. This pipe can swing f r e e l y around the p i v o t i n g point. The period o f the weight i n the pipe is adjusted to around one-half the period o f swinging.

Here, five cases are exainined: (1) The weight is released f r o m the l o w position. (2) The weight is released f r o m the high position. (3) The weight is fixed at the lowest position. (4) The weight is fixed at the balanced position. (5) The weight is fixed at the high position. For each case, the pipe is released f r o m the same i n i t i a l angle.

Roughly speaking, f r o m F i g . 2a, i t can be said clearly that the decreasing rate o f the swinging amplitude o f cases 1 and2 is larger than that o f cases 3, 4, and 5. Oscillating

Measured Distaiice is

transformed to angle » Pivoting Point

• Spnng - Weight

In Acrylic Pipe

3 Principles of V W S

3.1 Coordinate system and equation o f m o t i o n

F r o m the simple experiment i n the previous section, i t is clear that the linear motion o f a mass i n a rotating tube generates some damping effect. Here, the piinciples o f V W S that generate dainping effect are presented b y physical consideration. For simplicity, pure r o l l i n g m o t i o n is considered.

Equation 1 is the general f o r m o f pure ship-rolling. 0 is the r o l l angle ( i n rad) as shown i n F i g . 3, the t i m e deiiv-ative o f r o l l i n g angle is d(^/d/, k is linearized damping coefficient, W ( i n N e w t o n ) is the displacement, G M is the height o f metacenter, is moment o f inertia, J^^ is added moment o f inertia b y fluid and M is external exciting moment mainly by waves. O f course, i f M = 0, then this represents pure free r o l l i n g .

At ( 1 )

Fig. 1 Principal experiment f o r Vertical Weight Stabilizer

A s shown i n F i g . 3, i n the case o f V W S , a w e i g h t (mass is m k g and m is included i n the total mass) is m o v e d up and d o w n along the rotating straight guide. The position o f the weight is i d e n t i f i e d by the distance I f r o m the center o f rotation, / j or I2, f o r example. So, this vertical m o t i o n o f a mass changes the moment o f inertia /xx i n t i m e , then generating additional forces and moments.

3.2 A d d e d effects o f V W S on the equation o f m o t i o n

A b o u t the V W S , i n the resting condition o f the ship, the weight o f the straight guide, actuator m o v i n g the weight, and movable weight are included i n the o r i g i n a l ship weight and moment o f inertia. I n the next section, the additional effect o f a m o v i n g weight is discussed.

294 J Mar Sci Teclinol (2014) 19:292-301

Fig. 2 a Time history of swinging angle o f the pipe by the systein of Fig. 1. b Time history o f swinging angle of the pipe and weight motion inside the pipe corresponding to a

, 1 . W E I G H T I S R E L E A S E D F R O M L O W P O S I T I O N "0 10 2 0 3 0 4 0 5 0 6 0 7 0 ^ 2 . W E I G H T I S R E L E A S E D F R O M H I G H P O S I T I O N 1 1 0 0 to 2 0 3 0 4 0 5 0 6 0 3 . W B I G H T I S F I X E D A T L O W P O S I T I O N 130 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 4 . W E I G H T I S F I X E D A T B A L A N C E D P O S I T I O N "O 1 0 2 0 3 0 4 0 5 0 6 0 „ 5 . W E I G H T I S F I X E D A T H I G H P O S I T I O N 7 0 130 TiiiE [sec] I . W E I G H T I S R E L E A S E D F R O M L O W P O S I T I O N - 1»^ I'l I'l I*" I ' l ' S w i n g a n g l e W e i g h t m o t i o n 1 , 1 . ' 0 5 10 2 . W E I G H T I S R E L E A S E D F R O M H I G H P O S I T I O N 15 9 0 6 0 3 0 0 - 3 0 - 6 0 9 0 o S w i n g a n g l e W e i g l i t m o t i o n 2 0 - | 9 0 - 6 0 - 3 0 , 0 - 3 0 ' - 6 0 ; 9 0 3 ^ 3 3

3.2.1 Additional effects ofthe variation of moment of inertia on damping term

I f the w e i g h t o f V W S moves along the r o t a t i n g straight guide, the angular m o m e n t u m L around the r o t a t i n g axis is expressed as E q . 2. Here, the term mf is the m o m e n t o f i n e r t i a / by the w e i g h t m at an instant t, then / is the f u n c t i o n o f t i m e t and / expressed as lit) = mlitf. L = m- f d ^ dt (2) 2m • I dL_d_

d7~ df

d/ d0

Angular momentum L{t) is defined as / ( ) ( d ( / ) / d f ) , and the time derivative o f L{t) becomes the reaction moment around the center o f rotation. So, by adding dU dt expressed by Eq. 3 to the Eq. 1, we can obtain the

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Fig. 3 Coordinate systein. X axis is directing to forward

l o l l i n g equation o f motion including the effect o f V W S . T o clearly show the effect o f V W S , we separated that part. I n the case of V W S , this derivative generates t w o terms expressed as the second line o f E q . 3. The second or the t h i r d line o f the right hand side o f Eq. 3 is the additional inertial term, and this term has an effect o f depressing the roUing motion, l i k e the usual moment o f inertia.

I n the case o f the m o v i n g weight, additional damping-Uke terms, including dcp/dt, also appear i n Eq. 3. I f the term dl/dt becomes positive sign, then energy dissipation occurs regardless o f the sign of dcp/dt. So, f o r the purpose o f m o t i o n depression, a longer duration o f a large positive d//df value is better. I n case the term dl/dt becomes negative, energy absoiption occurs and r o l l i n g m o t i o n becomes large. T o m i n i m i z e the effect o f the negative damping, the absolute value o f negative d//d/ should be made m a x i m u m , during w h i c h dfp/dt becomes around zero. T h i s means that the weight should be moved upward at m a x i m u m speed around the t i m i n g that the r o l l i n g angular velocity becomes m a x i m u m (d(f)/dt — m a x i m u m ) , and moved d o w n w a r d at m a x i -m u -m speed at the end o f both swings o f r o l l i n g (dcp/dt = 0).

The term 2m{dI/dt){d4)/dt){=2muo:i) is the same expression as usual C o r i o l i ' s force, "u" is the linear speed o f the weight along the guide. I n the above C o r i o l i ' s term, additional lever / appears, and this becomes the expression o f the dimension o f the moment. Usually, C o r i o l i ' s force is described as a virtual effect, but the m o v i n g weight i n a rotating guide generates the same but real effect, disturbing the rotation of the guide, and this becomes the anti-rolling moment.

3.2.2 Ejfects ofthe variation of CG on the restoring term

The height of the center o f gravity C G is changed according the weight position o f V W S . Based on the initial position o f the m o v i n g weight, the deviation o f C G (written

as G G ' ) can be expressed by E q . 4 using the deviation o f the weight l{t) and the acceleration o f gravity g.

G G ' . ^ f ) (4)

The w h o l e weight of the V W S system w i t h the m o v i n g weight is included i n the ship displacement VV. Then the restoring moment by the weight movement can be expressed as Eq. 5. Here, GM is the height o f the meta-center.

Restoring moment = ( W ) { G M - GG'{t)}(j) (5)

3.2.3 Effect ofthe variation of CG on the damping term

The movement o f C G affects the damping term. This is not the hydrodynamic effect, but the apparent effect through the deviation o f the moment o f inertia o f r o l l i n g . D a m p i n g coefficient K, w h i c h expresses the equivalently linear damping o f the E q . 1, can be written as Eq. 6. is the so-called B e r l i n ' s A^-coefficient, represenfing the quadratic expression o f the curve o f extinction o f r o l l i n g .

m = - ^ ^ ^ + -/A-A- +

A7,,(0) •

Here, 4^. is the total moment o f inertia o f the ship, i n c l u d i n g the added mass moment o f inertia by the V W S w i t h the weight at lowest position. Jxx is the added moment o f inertia by fluid m o t i o n . A/,,, (0 is the deviated moment o f inertia by the m o v i n g weight and is the m a x i m u m r o l l i n g angle i n the curve o f extinction. Then, k becomes a f u n c t i o n o f time. Natural r o l l i n g period T^on also becomes a f u n c t i o n o f time, because restoring moment and moment o f inertia are both time dependent.

O f course, strictiy speaking, A' w i l l be also changed according the instant position o f the weight, but we assumed the deviation is small. Finally, it should be noticed that i n Sect. 3.2, the e f f e c t o f centrifugal force o n r o l l i n g moment is neglected, because centrifugal force does not affect r o l l i n g moment directly.

3.3 Evaluation o f the effect o f V W S on r o l l i n g moment

The effect o f V W S on r o l l i n g depression can be expected f r o m t w o points o f view. Firsfly, by the vertical movement o f a weight, additional damping appears as described i n Sects. 3.2.1 and 3.2.3. B y the second point o f v i e w , the deviation o f the moment o f inertia and the r i g h t i n g arm results i n the change o f the natural period o f r o l l , and finally results i n the avoidance o f resonance r o l l w i t h waves. So, i n the second case, fast movement o f a weight is not needed. Only the slow change o f the mean position o f the weight, not responding to the i n d i v i d u a l swing o f r o l l , can change the natural period of f h e r o l l .

296 J Mai- Sci Technol (2014) 19:292-301

I n the first case, rapid decrease o f large r o l l i n g due to resonance w i t h wave or due to the external inoment by gust w i n d , f o r example, is expected by additional damping. I n this case, rapid movement o f the weight is necessary.

Here, we evaluate the effect o f the first case. The resulting energy dissipation, during one swing, expressed as Evws by V W S , is evaluated by the f o l l o w i n g equations.

Evws = Ei+Ej (7) Here, 0 ?'roll 4yvio • A / v , . ( f ) (8) (9)

Troll is the r o l l i n g period and T^oim is the natural r o l l i n g period without the s h i f t o f the weight. Energy dissipation is obtained by m u l t i p l y i n g angular velocity and integrated b y time to the dissipation-related moment term o f the equation motion. Here, we adopted A'lo (A'^ coefficient at 10°), con-sidering pre-experiments and actual sea experiments.

On the other hand, dissipated energy by the h u l l m o d o n w i t h bilge keel can be expressed as

I S H I P

4N 10 o l l B

d(/)"l dcj)'

'"dFJ d7.

dr

Using Eq. 7 and 10, Eq. 11 can be defined. _ £'vws

EsHW

(10)

(11) This is the ratio o f dissipated energy by V W S to that by without movement o f V W S , and we use this as an index o f the effect o f V W S .

4 L a b o r a t o r y experiment using a small rowing boat

4.1 V W S f o r small boat

F i g . 4 Small boat for experiment. Weight is now at highest position

• Chain .,.

. Ivlotor and sprocl<et Lift up condition

Stored condition'

F i g . 5 Zipper-liice Z i p Chain. Right is chain itself, in separated and

united condition

Before carrying out the actual sea trials, we c a n i e d out laboratory experiment i n the t o w i n g tank o f Y o k o h a m a National University ( Y N U ) ( L = 100 m , B = 8 m, d — 3.5 m ) , using a small r o w i n g boat. B y this experiment we could c o n f i r m the system, especially the feedback control system. The mechanism o f V W S is very simple, as can be seen i n F i g . 4. I n the vertical guide frame, there is a vertical actuator called Z i p - C h a i n (a small type is shown i n Fig. 5). This is composed o f t w o zipper-like chains. T w o separated chains are m o v e d by a servo motor and come

together, and finally stand up by themselves w i t h o u t sup-port ( f o r applying this to V W S , soine additional guiding system is preferable). Thus, the vertical linear m o t i o n can be realized. This actuator can inove a small weight verti-cally w i t h high speed in along stroke. I n the case o f this experiinent, ship length L — 2.8 m , breadth B = 1.6 m , and displacement W — 167 k g f , i n c l u d i n g V W S w i t h 7 k g m o v i n g weight. Height o f the guide is 2.5 m . Double amplitude o f weight movement is 0.6 m . W e changed the height o f the initial position o f the weight i n f o u r cases, but

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only show the result f o r the case o f 1.71 m f r o m the base o f V W S .

4.2 C o n t r o l method

As a control method, we adopted a conventional propor-tional derivative (PD)-feedback system. This can be expressed as f o l l o w s .

l{t) = lo+(Kp-(l) + K d - ^ ) (12)

Here, /q is the i n i t i a l position o f the weight, (j) is the instantaneous r o l l i n g angle (regular or irregular m o t i o n ) , and coefficients Kp, Kd are so-called gain f o r each o f the proportional and differential terins. I n the case o f regular motion, (p = (pQ sm{cot) and d(j)/dt = (pQCO cos{cot), then Eq. 12 becomes

= h + Kp • sin(rof) -1- Kd • (})qCO cos{cot)

r 0 (13) = k + (po\/Kp^ + (Kdojfsm{o]t + d)

Here, 5 = Xm-\KplKda).

So, we can understand that by changing Ks and Kc, phase lag (defined i n the case o f regular inotion) o f the weight m o t i o n to the r o l l i n g angle can be changed.

I n the actual case, we tried to control the m o t i o n o f the weight, as expressed b y the Eq. 14.

l{t) = /o - f Ks{Kp -(jf + Kd- dcp/dtf (14)

Here, another coefficient Ks, adjusting the stroke o f the weight, is introduced. For the case o f regular m o t i o n , this is written i n simple manner as,

Z(0 = /o + A / - s i n 2 ( c ü „ / - f - < 5 ) (15) Here, Al is the amplitude o f the m o t i o n o f the weight. 5

is the phase lag between the m o t i o n o f the weight and r o l l i n g angle. Squared sine is introduced i n order to realize the t w o movements o f the weight i n one swing o f the r o l l , as already required. The squared sine terin o f E q . 15, makes sin(2(co/' - f S)) tenn.

For realizing the t w o movements o f the weight i n a single s w i n g o f r o l l i n g motion, there is another expression. For example, the absolute value o f sin(ff)t - f 5) can be used, because this expression generates two positive peaks i n one swing o f r o l l i n g . B u t we adopted an expression (14, 15) f o r obtaining smoother movement o f the actuator. Furthermore, o p t i m u m phase lag 5 is estiinated and adjusted i n order to make the dissipated energy m a x i m a l by numerical calculation.

As an exainple, the estimation o f the effect o f phase lag to the dissipated energy (Eq. 7) is shown i n F i g . 6. The index o f the e f f e c t o f V W S defined by Eq. 11 is shown i n F i g . 7.

Figure 7 coiTesponds to the case o f Ship-A, described i n the section on the sea t r i a l . L o o k i n g at this figure, we can recognize that the o p t i m u m phase lag between the weight m o t i o n and the rolUng m o d o n is around -|-50° (advanced phase), and a 60 % effect o f that b y ship hull w i t h bilge keel w i l l be obtained. The tendency o f the o p t i m u m phase lag is similar i n cases o f other ships. O f course, this is the result o f theoretical calculation w i t h some assumptions, so some tuning or a trial and eiTor method is needed f o r the actual system. Furthermore, i f we can use actuators w i t h higher speeds, larger effects w i l l be expected.

4.3 Case o f free r o l l

I n the case o f the free r o l l on still water, the time history o f the small boat is shown i n F i g . 8. Upper (a) is the r o l l angle i n a case without control by V W S . M i d d l e (b) is the case w i t h control. Bottom (c) is the movement o f the weight. A s described, figure (c) shows the t w i c e frequency comparing w i t h that o f (b). I n i t i a l r o l l angle o f (a) is a l i t t l e larger than that o f (b). But i f we compare the t i m e history o f (a) and (b) after the time o f the same r o l l i n g amplitude can be recognized, the large decreasing rate o f (b) is evident. That means the effect o f V W S is significant.

4.4 Case o f r o l l i n g i n irregular beam waves

The results o f r o l l i n g i n the case o f irregular beam waves (mean wave period is 1.9 s, significant wave height is 0.05 m ) are shown i n F i g . 9. F r o m the top, r o l l angle w i t h o u t control, r o l l angle w i t h control and power spectra

1500

Phase 6(deg)

Fig. 6 Estimated dissipated energy E i , E T and E^ws (Ship-A)

Pliase6(deg)

Fig. 7 Ratio o f dissipated energy Evws to Es^ip (Ship-A)

298 J M a r Sci Teciinol (2014) 19:292-301

of both cases are shown. F r o m the area o f power spectra, i t can be said that significant r o l l double amplitude is depressed f r o m 19.7° 'to 12.2°, and the decreasing rate becomes about 40 % . a ^ ^ R o l l A n g l e ( W i t h o u t C o n t r o l ) b 10 3 ° -5 -10 C 0.5 0.2 0 20 30 40 R o l l A n g l e ( W i t h C o n t i o l ) L A - A _ A _ ^ A A A A A t A A A A A . ' A k Ji.'t). i A. w 20 3 ) 4 ) 50 60 7 ) V W S W e i r f i t Position t[sec]

Fig. 8 Results o f case o f free r o l l (small boat). Upper (a) is the roll

angle i n a case without control by V W S . M i d d l e (b) is the case w i t h control. Bottom (c) is the movement o f the weight

Roll angle Without control 10 0 -10 10 0 -10 0 . 5 0 1 ' 1 ' 1 ' 1 1 1 1 1 1 j 1 1 1 1 1 j 1 1 1 1 1

| H I | | I I ^ ^

Roll angle With control 1 1 1 1 1 1 , -Weight motion 1 _{1 1}

.iAiyA

|lLji|

Power spectrum o f r o i l angle

Ü 6 0 2 0 T W i t h c o n t r o l W i t h o u t c o n t r o l I ' i l l l H l i i i i i f t i M i m . i i / i i i . i i i n i i i ^ m m i i 0 2 4 6 8 OJ [rad/sec]

Fig. 9 Results (small boat) in the case o f irregular beam waves. The

mean wave period is 1.9 s, significant wave height is 0.05 m. From the top, roll angle, roll rate, weight motion and spectra o f r o l l angle are shown

As already described i n Sect. 4.2, P D control can be also used i n the case o f irregular m o t i o n , by using the instan-taneously measured r o l l i n g angle and r o l l i n g angular velocity. W e d i d n ' t carry out numerical simulations i n irregular waves f o r obtaining the optimal gain f o r P D control, but the results i n a regular wave case w i l l be roughly applicable, because m o t i o n w i t h the natural period of r o l l strongly appears even i n irregular waves, as usually experienced.

5 Prototype V W S for actual ship

5.1 Used ships f o r sea trial

W e designed and constructed a prototype V W S , and car-ried out sea trials applying to t w o small ships o f similar size. One is Ship-A and the other is Ship-B. Principal dimensions are shown i n Table 1. Section shapes and V W S mounted on the deck are shown i n F i g . 10. The mechanism o f V W S is c o m m o n f o r both ships, but its height is d i f -ferent, considering the possible dead weight and stability.

5.2 Construction o f prototype V W S

The Vertical W e i g h t Stabilizer is composed o f thi-ee seg-ments: the guide segment, the actuator segment and the controller segment. The guide segment is composed o f three units ( S h i p - A ) or two units (Ship-B). The length o f one u n i t is about 2 m . The guide segment is a mast-shaped circular tube, and is used f o r guiding the m o v i n g w e i g h t i n linear motion. The guide segment is held by wire-stays, considering the dynamic tension generated by the moment f r o m C o r i o l i ' s force when the weight is m o v e d i n r o l l i n g condition.

For the actuator segment, we adopted the special linear actuator Z i p - C h a i n . Z i p - C h a i n realized hnear m o t i o n

Table 1 Principal ditnensions

Ship name Ship-A Ship-B

Material A l u m i n u m Steel

Ship type Deep V Tug boat type

Gross tonnage (ton) 4.9

Length (oa) (m) 10.1 9.5

Breadth (m) 2.69 2.40

Depth (m) 0.90 1.07

Lightship condition (without V W S )

Displacement (kg) 5,238 8,639

Draft (tn) 0.455 0.758

K G (m) 0.867 0.869

G M t (m) 1.684 0.549

J M a r Sci Teclinol (2014) 19:292-301 299

Fig. 10 Ship-A (left) and Ship-B (right) f o r sea hials

(stroke is 3 m) by a zipper-like chain w i t h relatively h i g h speed (3 m/s), holding a weight (185 k g ) . Electric power is supplied f r o m outside (Ship-A) or by an on-board generator (Ship-B)

The controller receives signals f r o m sensors (roll angle, angular velocity, vertical accelerometer and weight posi-tion), calculates the position o f the weight, and sends signal to the actuator.

The weight o f ino v i n g mass is about 3 % o f ship dis-placement. The power needed f o r d r i v i n g the weight is not so much. For down stage o f the weight, energy o f position can be recovered to the actuator. The peak value was about 5.3 k W f o r the sea trial. This is very small compared to that o f the prime mover o f the ship. B u t the absolute w e i g h t becomes very large f o r large ships. Therefore, mainly f o r safety reasons and limitations o f the size o f a usable actu-ator, the possible ship size w i l l be l i m i t e d to small ships.

5.3 Sea trial at Lake B i w a (Free r o l l near the birth)

The first sea trial evaluating the V W S was carried out using Ship-A at Lake B i w a . A t that time, it was forecasted that a typhoon would pass near the trial site, so only the f r e e -r o l l i n g decay test could be done nea-r the bi-rth, befo-re the typhoon came. I n F i g . 1 1 , the r o l l i n g m o t i o n by the V W S became smaller, as was the case f o r the laboratory exper-iment using a small boat. R o l l i n g inotion was generated b y

-10,

-Wei^it position

Free Roll Start

VWSl 12 Fixed al low nositioii

WVVAAWWx/

F i g . 11 Time history ( V W S l 12 & V W S 121) of Ship-A

F i g . 12 Sea trial near the Harbor of Yokohama

p u l l i n g and releasing a w i r e connected to the t o p o f the mast. A s can be seen i n F i g . 11, resonant r o l l was gener-ated f o r obtaining r o l l i n g motion.

5.4 Sea trial near the Harbor o f Y o k o h a m a

The second sea trial f o r thre free r o l l test and experiment i n irregular waves was earned out near the Harbor o f Y o k o -hama ( F i g . 12). The free r o l l test on s t i l l water was also conducted near the shore. Decrease o f r o l l i n g m o t i o n was confirmed, as was the case w i t h the L a k e B i w a and labo-ratory experiments. Regarding an open sea trial i n i i T c g u l a r waves, the condition o f sea waves was not enough f o r evaluating the f u l l characteristics o f our V W S , but rela-t i v e l y successful darela-ta were obrela-tained ( F i g . 13).

B y m a k i n g the switch on or o f f , under the same sea conditions, both " w i t h c o n t r o l " and " w i t h o u t c o n t r o l "

300 J M a r Sci Teclinol (2014) 19:292-301

Fig. 13 From the top, r o l l angle, r o l l rate and weight motion, the power spectra o f roll {left) and r o l l rate (right) in inegular seas (Ship-B) are shown to 3 0 - 1 0 R o l l a n o l e W i t h c o n t r o l • - W i t h o u t c o n t r o l 3 0 S, 15 "So 0 • S - 1 5 ^ - 3 0 1.5 i 1 1 I 1 1 1 1 1 1 1 R o l l r a t e I ' l ' Jj i l l ' J k i l l l l ' lii ll Jl i ' I ik 111 1 ' 1 ~ 1 1 1 1 1 1 , 1 1 II 1 111, 1 , 1 Jj i l l ' J k i l l l l ' lii ll Jl i ' I ik 111 1 ' 1 ~ 1 1 1 1 1 1 , 1 1 II 1 111, 1 , 1 W e i g h t m o t i o n 1 ' ' ' 1 ' 1 ' 1 ' 1 . y r t ..1.1 i l . i . > . i i n , i< . » i n „ . i< l . . l l l l ll I'll 1 i i l i i n . i l l l l l . ll ,J -2 0 10 h too P o w e r s p e c t r u m o f r o l l a n g l e 2 0 0 3 0 0 W i t h c o n t r o l W i t h o u t c o n t r o l -so 2 0 10 4 0 0 P o w e r s p e c t r u m o f r o l l r a t e 5 0 0 Tiine [sec] 1 2 3 03 [ r a d / s e c ]

cases were directly compared. From the top, r o l l i n g amplitude (°), r o l l i n g rate (°/s), and the m o t i o n o f the weight ( m ) , are shown. The power spectra o f r o l l i n g angle are also shown. F r o m those figures, the significant value o f r o l l angles is 7 . 2 2 ° ( w i t h control) and 8.87° (without con-trol). Therefore, the reduction rate is 19 %. This value is not very large, but the reason is that sea condition was not severe f o r the r o l l o f Ship-B. B u t , i f we notice the reduction rate around the peak value o f the energy spectrum, the effect becomes large. L o o k i n g at the peak values o f the power spectrum o f r o l l angle i n F i g . 13, its ratio is around 1/3 i n the case o f m o v i n g V W S , so i f we consider the square root o f this value, the decreasing rate o f the r o l l amplitude around the natural frequency o f the r o l l w i l l be about 40 %. This value is close to the result o f laboratory tests.

6 Conclusions

A n t i - m o t i o n devices are important f o r the freely oscillating floating ships and structures. I n the six modes o f ship motions, anti-rolling is very important f o r the safety and comfortable operation o f ships or ocean vehicles. The principle of V W S was invented 14 years ago w i t h suc-cessful results i n the experimental tank, but its actual use was d i f f i c u l t because we could not find an appropriate actuator. This time, f r o m the concept of V W S , we exam-ined its mechanism i n detail and constructed a [prototype V W S f o r an actual ship, applying an appropriate new

actuator. Furthermore, we carried out sea trials and the f o l l o w i n g results were obtained.

1. B y simple laboratory experiment, i t was shown that damping effect clearly appears by a l l o w i n g the m o t i o n of a mass i n a rotating tube.

2. The mechanism o f V W S was examined i n detail, showing and evaluating the equation o f pure r o l l i n g motion.

f-3. V W S f o r an actual ship was reaUzed by adopting a new compact, high-quality actuator called Z i p Chain. 4. As expected f r o m the laboratory experiments and

numerical calculations, the prototype V W S f o r an actual ship showed anti-rolling effects i n f r e e r o l l i n g . 5. I n irregular seas, f r o m the view p o i n t o f significant value, the reduction rate was not very h i g h , but looking at the reduction rate around natural frequency o f r o l l i n g , the reduction rate was about 40 % .

6. The needed weight of m o v i n g mass o f V W S is not large. It was around 3 % o f ship displacement. 7. The power needed f o r d r i v i n g the mass o f V W S is not

very high. The peak value o f power was about 5.3 k W for sea trials, and it was 2.5 % o f the power o f the main engine o f the ship being used.

A c k n o w l e d g m e n t s The authors want to express their gratitude to M r . Saji et al. o f the Tsubakimoto Chain CO. (Japan) who supplied Zip-Chain as an actuator o f our V W S , and to those o f Mokubei-Zosen CO. and Keihin Dock CO., L T D . f o r supporting us when catrying out the sea trial. W e also express our acknowledgment to the students o f our Sea and A i r Control Systetns Laboratory o f Y N U , w h o supported our project of V W S .

J Mar Sci Teclinol (2014) 19:292-301 301

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